Every Noetherian uniformly coherent ring has dimension at most 2
type: Item
instance of: scholarly article
title: Every Noetherian uniformly coherent ring has dimension at most 2
zbMATH Open document ID: 0533.13005
author: Shiro Goto
published in: Journal of Mathematics of Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: A commutative ring R is said to be coherent if each finitely generated ideal of R is finitely presented. R is called uniformly coherent if for any positive integer n and any nonzero homomorphism \(f:R^ n\to R\), ker f can be generated by \(\Phi\) (n) elements, where \(\Phi\) (n) is a nonnegative integer depending only on n. Sally proved that any two- dimensional Noetherian local ring is uniformly coherent [\textit{J. D. Sally}, ''Numbers of generators of ideals in local rings'' (1978; Zbl 0395.13010)]. This paper sharpens Sally's result as well as establishing the general converse, i.e., each Noetherian uniformly coherent ring has dimension at most two.
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13H99
zbMATH DE Number: 3845720
zbMATH Keywords: Noetherian ring
zbMATH Keywords: two dimensional ring
zbMATH Keywords: uniformly coherent commutative ring
zbMATH Keywords: number of generators of ideals
zbMATH Keywords: local ring
reviewed by: Ira Papick
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521559
OpenAlex ID: W1962785298
DOI: 10.1215/KJM/1250521559
description: scientific article; zbMATH DE number 3845720